# Rotation of vector in 3 directions

Discussion in 'Introductions' started by VicenteMMOS, Apr 22, 2022.

1. ### VicenteMMOS

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Apr 22, 2022
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Hello, everyone!

I have a quite simple question, but one which I didn't manage to find the answer myself, even trying to draw it in 3D cad software to help me visualize things! This is the problem statement:

suppose unit vector V is oriented along Z axis in a cartesian OXYZ system. Now, take another Oxyz system, such as its axes are rotated wrt the original cartesian system with angles theta, phi and psi, respectively. Theta is the angle between Z-z axes as viewed in front projection, phi is the angle between Z-z as viewed in a right projection, and psi is the angle between X-x as seen from the top projection. Give the xyz components of vector V in the Oxyz coordinate system.

The angle values are arbitrary, but fixed. I spent the entire day today trying to solve the math for this simple question, but I just couldn't find an answer! I know if we only have one angle, then the projected length of V is V.cos(theta), but when we have three angles, I just kept confusing myself with how to describe the coordinate systems, and find each projection! Please, help! =(

Thank you,
Vicente

VicenteMMOS, Apr 22, 2022

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